Mathematics Colloquium
Contact: Federico Ardila
Time and Location: Wednesdays, 4:10-5:00 pm in Thornton Hall 211.
Refreshments: 3:30 pm in Thornton Hall 935.
Past colloquia: videos and
abstracts.
Spring 2009 Dates: Feb 4 Feb 18 Mar 4 Mar 16 Mar 18 Mar 19 Apr 8 Apr 22 Apr 24 May 6
Sandor Kovacs
University of Washington
| TITLE: The geometric Mordell conjecture and higher dimensional generalizations, |
|
ABSTRACT:
Let X be a smooth complex plane curve defined by an equation of degree
at least 4 with integer coefficients. Mordell's conjecture states that
there are only finitely many points on X all of whose coordinates
are rational numbers. More precisely, this is (a special case of) the
arithmetic Mordell conjecture, proved by Faltings in the early 1980s
earning him a Fields Medal in 1986.
In this talk I will explain the geometric Mordell conjecture which is
an analogue of the above statement with integers and rational numbers
replaced by some natural geometric data. I will also explain how
the Mordell conjecture (in both the arithmetic and the geometric
cases) follows from another famous conjecture, that of Shafarevich,
and how these conjectures were proven by Manin, Parshin, Arakelov, and
Faltings.
Finally, I will mention recent progress towards various higher
dimensional generalizations of Shafarevich's conjecture. These include
results of joint efforts with various subsets of {Daniel Greb, Stefan
Kebekus, Max Lieblich}.
|
|
4:10 PM in TH 211 |
|
refreshments
served in TH 935 at 3:30 PM |
Burt Totaro
University of Cambridge
| TITLE: Algebraic surfaces and hyperbolic geometry. |
|
ABSTRACT: The intersection form on the group of line bundles on a complex
algebraic surface always has signature (1,n) for some n. So the
automorphism group of an algebraic surface always acts on hyperbolic
n-space. For a class of surfaces including K3 surfaces and many rational
surfaces, there is a close connection between the properties of the
variety and the corresponding group acting on hyperbolic space.
|
|
4:10 PM in TH 211 |
|
refreshments
served in TH 935 at 3:30 PM |
J. Maurice Rojas
Texas A&M University
| TITLE: To be announced. |
|
ABSTRACT: To be announced.
|
|
4:10 PM in TH 211 |
|
refreshments
served in TH 935 at 3:30 PM |
Rich Schwartz
Brown University
| TITLE: To be announced. |
|
ABSTRACT: To be announced.
|
|
4:10 PM in TH 211 |
|
refreshments
served in TH 935 at 3:30 PM |
Pamela Fong Symposium - Public Lecture
De Witt Sumners
Florida State University
| TITLE: Calculating the secrets of life: Mathematics in biology and medicine. |
|
ABSTRACT: The human body is an extremely complicated biological system. Spurred by spectacular recent progress, biology and medicine are experiencing an explosion of data. In order to convert this fire hose of data into usable knowledge, mathematics and computation (both old and new) are needed to build models and navigational tools. This talk will briefly discuss a few applications to show the impact that mathematics can have in biology and medicine: in the cell (understanding how enzymes operate on DNA); in the heart (controlling fibrillation); and in the brain (understanding brain function).
|
| TITLE: DNA topology. |
|
ABSTRACT: Cellular DNA is a long, thread-like molecule with remarkably complex topology. Enzymes that manipulate the geometry and topology of cellular DNA perform many important cellular processes (including segregation of daughter chromosomes, gene regulation, DNA repair, and generation of antibody diversity). Some enzymes pass DNA through itself via enzyme-bridged transient breaks in the DNA; other enzymes break the DNA apart and reconnect it to different ends. In the topological approach to enzymology, circular DNA is incubated with an enzyme, producing an enzyme signature in the form of DNA knots and links. By observing the changes in DNA geometry (supercoiling) and topology (knotting and linking) due to enzyme action, the enzyme binding and mechanism can often be characterized. This talk will discuss how topology can be used to analyze the results of these DNA experiments.
|
| TITLE: Discriminating between long memory and change-point models. |
|
ABSTRACT: Over the last two decades long memory time series have become an
established modeling tool in many areas of science and technology,
including geosciences, medical sciences, telecommunication networks
and to some extend financial econometrics. It has however been
recently realized that practically all statistical procedures intended
to detect and estimate long memory give spurious results if a time
series without long memory is perturbed by nonstationarities, like
trends or breaks (change-points). For example, if a mean of a short
memory time series changes, a test for the presence of long memory
will incorrectly indicate that the time series has long memory.
Similarly, a test for the presence of change point, will incorectly
show that that a change point is present if the time series is
stationary with long memory. A growing body of research which has
accumulated over the last decade is concerned with finding and
illustrating cases of such spurious inference, without addressing the
issue how to choose between the two modeling approaches.
After a suitable introduction,
we will discuss two new statistical tests aimed at distinguishing
between the two approaches and apply them to a financial and a
hydrological time series. The talk will focus on the ideas rather than
technicalities and will be accessible to undergraduate math/stat
majors and graduate students.
|
|
4:10 PM in TH 211 |
|
refreshments
served in TH 935 at 3:30 PM |
Andisheh Mahdavi
Department of Physics
San Francisco State University
| TITLE: Dark and Luminous Matter in Clusters of Galaxies. |
|
ABSTRACT: Clusters of galaxies are dominated by dark matter, the invisible stuff
that makes up most of the ordinary mass of the universe. We can see the
gravitational effect of this dark material on the orbits of cluster
members, the thermodynamics of the hot gas, and the lensed shapes of
galaxies behind the cluster. I will review the ongoing efforts to
constrain the properties of dark matter on the scale of millions of
lights years. In particular, I will discuss an unusual, massive, X-ray
bright core nearly devoid of galaxies at the heart of the "cosmic
trainwreck" (the Abell 520 extreme cluster merger), and will explore
its implications for our understanding of the fundamental nature of
dark matter.
|
|
4:10 PM in TH 211 |
|
refreshments
served in TH 935 at 3:30 PM |
Howard Masur
University of Chicago
| TITLE: To be announced. |
|
ABSTRACT: To be announced.
|
|
3:10 PM in TH 211 - NOTE THE UNUSUAL TIME |
|
refreshments
served in TH 935 at 2:30 PM |
Previous semesters.
Fong Symposia.
